RE: size_question_encore

[Marta Bunge <martabunge@hotmail.com>]

Dear Andre,

I believe that you misunderstood the comment made in Bunge-Hermida (2011) concerning model structures. In particular, I do not know what you meant by your saying "I disagree with your conclusion". We say precisely in Section 3 (Remark 3.6) that the two model structures mentioned - namely the Joyal-Tierney and the Lack model structures on Cat(S), S a Grothendieck topos, are different, and why. I think then that we agree. 
Best,Marta
 

> From: joyal.andre@uqam.ca
> To: categories@mta.ca
> Subject: categories: RE: size_question_encore
> Date: Sun, 10 Jul 2011 09:30:07 -0400
> 
> dear Marta,
> 
> I apologise, I had forgoten our conversation!
> My memory was never good, and it is getting worst.
> 
> You wrote:
> 
>  >No, I am not thinking of the analogue of Steve Lack's model  
> structure since, strictly speaking,
>  >it has nothing to do with stacks. Comments to that effect (with  
> which Steve agrees) are included
>  >in the Bunge-Hermida paper. It was actually a surprise to discover  
> that after trying to do what
>  >you suggest and failing.
> 
> I disagree with your conclusion. I looked at your paper with Hermida.
> We are not talking about the same model structure. The fibrations in  
> 2Cat(S) defined
> by Steve Lack (your definition 7.1) are too weak when the topos S does  
> not satify the axiom of choice.
> Equivalently, his generating set of trivial cofibrations is too small.
> 
> Nobody has read my paper with Myles
> <A.Joyal, M.Tierney: Classifying spaces for sheaves of simplicial  
> groupoids, JPAA, Vol 89, 1993>.
> 
> Best,
> André
> 
> 
> 

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